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I always wonder who invented properties of addition. The usefulness of properties of addition can be seen during practice. There are many algebraic tools, but properties of addition are so interesting that while practicing properties of addition you will derive fun from it.

Sometimes we need to add long strings of numbers without using a calculator. No worries, properties of addition will work for you. For example, you might be asked to add 38 + 43 + 62 + 11 + 17. This computation is difficult to calculate without a calculator. But the assignment can be made easier by simply knowing easy properties of addition.

p>The following lines will discuss properties of addition briefly so that you can come across the functions of these properties of addition.

## Properties of Addition – Commutative Property

This form of properties of addition, known as the Commutative Property, maintain that for any numbers (‘a’ and ‘b’), the following is true for all times:

a + b = b + a

For example, 4 + 5 = 5 + 4. We can understand that this is true because 4 + 5 = 9 and 5 + 4 = 9, as well as 4 + 5 and 5 + 4 are on a par with each other as proved by one of the properties of addition. Another way to understand the Properties of Addition (commutative property) is as following: if you have a dollar and a quarter in your pocket, and you add them together, you will end up with the equal amount of money whether you add the dollar to the quarter or the quarter to the dollar.

With the help of (properties of addition) Commutative Property, we can always add two or more numbers irrespective of their order. It is quite useful too, because you might find it easier to add numbers in a different order than the given order. In the above example, it looks like a lengthy task to add the numbers from left to right (you can try it). However, with the help of (properties of addition) Commutative Property, you can change the order of the numbers in the following expression

38 + 43 + 62 + 11 + 17 = 38 + 62 + 43 + 17 + 11

The new expression is much easier to calculate, because 38 + 62 = 100 and 100 + 43 + 17 = 160 + 11 = 171. You can observe that it is easier to add numbers to numbers, with the help of (properties of addition Commutative property, which end in "zero". This computation can be made further easier to calculate with the help of (properties of addition) Associative Property

### Properties of Addition – Associative Property

Another property from the properties of addition is known as the Associative Property, which maintains that for any numbers ( a, b, and c), the following is true for all times:

(a + b) + c = a + (b + c)

For example, (3 + 5) + 6 = 3 + (5 + 6). We can understand that this is factual because (3 + 5) + 6 = 8 + 6 = 14 and 3 + (5 + 6) = 3 + 11 = 14, hence (3 + 5) + 6 and 3 + (5 + 6) are equal to each other due to the beautiful act of properties of addition.

Keeping properties of addition in action, we can once again think about the example of money: if someone has a nickel and a dime in his left pocket and a quarter in his right pocket, he will have exactly the same amount of money if he takes the dime out of his left pocket and put it in his right pocket with the quarter.

In this way, not only we can add numbers in any order by using one of the amazing properties of addition, but also can add pairs of numbers within the given expression before addition. In other words, we can place parenthesis around the numbers (two or more), and then add them separately. As we have already discussed, we can reorganize the numbers by using the Commutative Property (properties of addition). And then using the Associative Property, from properties of addition, for adding them in pairs.

38 + 43 + 62 + 11 + 17 = (38 + 43) + (62 + 11) + 17 = 81 + 73 + 17 = 171

You can observe that it's easier to add these three numbers in your mind than to add the initial five numbers one by one. You also can observe that both methods yield the same answer and that is 171. This proves the efficacy properties of addition.

### Properties of Addition – Easy steps to remember

An easy step to remember properties of addition is that when the Commutative Property is needed to be applied, check that only addition is involved and numbers can be moved (or “commuted”) to anywhere in the expression. In the same way, when the Associative Property (properties of addition) is needed to be remembered, remember that the numbers that you add together can be “associated” with each other.

Another thumb rule to recall is, while learning properties of addition, when you want to decide which property to use among the properties of addition, first look for numbers that can be added up to multiples of 10. Add these numbers first as this is easy.

### Properties of Addition - Identity Property

Besides all above defined properties of addition, one final property that is also very useful in algebra is known as the Identity Property, which explains that for any number a, the following will always be true:

a + 0 = a or 0 + a = a

Amongst other properties of addition, the Identity Property tells us about the identity of a number, as is obvious from its name. It says that a number does not change its identity when 0 is added to it. For example, 16 + 0 = 16. 0 + 12 = 12. Or, we can say that if someone has zero dollars in his pocket, the amount of money he possesses does not change.

### Usage of Properties of Addition

The Properties of Addition can be used in any order. At the moment, these properties of addition are considered as extremely useful while adding the long strings of numbers, because they make this task easier.

Below are some examples to show how the Properties of Addition can make mental math easy:

•

Properties of Addition – Use of Commutative Property

Example: 12 + 57 + 88 = ?

12 + 57 + 88 = 12 + 88 + 57

Pick Commutative Property from properties of addition to find 12 + 88 + 57 = 100 + 57 = 157
•

Properties of Addition – Use of Associative Property

Example: (13 + 31) + (9 + 7) + 5 = ?

(13 + 31) + (9 + 7) + 5 = 13 + (31 + 9) + (7 + 5)

13 + (31 + 9) + (7 + 5) = 13 + 40 + 12 = 65
•

Properties of Addition – Example. 34 + 13 + 2 + 6 + 3 + 17 = ?

Use of Commutative Property: 34 + 13 + 2 + 6 + 3 + 17 = 34 + 6 + 17 + 3 + 2 + 13 = 40 + 20 + 15 = 60 + 15 = 75

Use of Associative Property from properties of addition: 34 + 13 + 2 + 6 + 3 + 17 = (34 + 6) + (17 + 3) + (13 + 2) = (34 + 6) + (17 + 3) + (13 + 2) = 40 + 20 + 15 = 75

In mathematics these are one of the simplest numerical tasks. Thanks to properties of addition, in the modern days the addition of fairly small numbers is even available to toddlers; the most basic assignment, that is 1 + 1, can be performed by a five months old. We all learn to add numbers in our early education with the help of properties of addition, where students impart a training to add numbers in decimal system. The training starts with tackling single digits and progressively undertaking more difficult tasks with the aid of properties of addition. Historically we find mechanical aids from the ancient abacus which has turned to modern computers, however, studies are still last to find effective implementations.

Addition is an ancient basic mathematical process in existence, so as the properties of addition. It is also known as one of the very first mathematical operations people come into contact in their early babyhood, which lead to the invention of properties of addition..

The properties of addition are extremely useful tools in making the basic and long string mathematical addition easier. Understanding the properties of addition can improve your mental math exercises.

• From the above-mentioned details we learn the following useful roles of properties of addition.
• Properties of Addition provide us with an ease in mathematics.
• Properties of Addition provide us help to add long strings of numbers.
• Properties of Addition provide us aid to calculate without a calculator.
• Properties of Addition provide us helping hand to commute numbers.
• Properties of Addition tell us how to associate numbers.
• Properties of Addition give us liberty to first add numbers with multiples of 10.
• Properties of Addition extend a hand when we are in impasse of mixed figures.
• Properties of Addition are an easy tool to learn.
• Properties of Addition make calculation interesting.
• Properties of Addition make mathematics fun.
• Properties of Addition let us make a difficult calculation easy.
• Properties of Addition – they are only three to practice.
• Properties of Addition can boost your ability to solve very demanding math problems.
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